Problem 2 25 pts a block of mass m 54 kg at rest on a

Problem 2 (25 pts.): A block of mass M = 5.4 kg, at rest on a horizontal frictionless table, is
attached to a rigid support by a spring of constant k = 6000 N/m which is initially uncompressed.
A bullet of mass m = 9.5 g and velocity

v
of magnitude 630 m/s strikes and becomes embedded
in the block. This compresses the spring and sets block and spring in simple harmonic motion.
Determine:
a) ( 8 pts. ) the speed of the block immediately after the collision.
b) ( 9 pts. ) the amplitude of the harmonic motion.
2
c) ( 8 pts. ) the frequency of the harmonic motion.
M

Problem 3 (25 pts.) The figure to the right shows a block S
with mass M . The block is free to move along a horizontal
frictionless surface and connected, by a massless cord that
wraps over a frictionless pulley with mass m and radius
( I=mr
2
/2) to a second block H also of mass m . The hanging
block H falls as the sliding block S accelerates to the right.
a) ( 6 pts.) Draw force diagrams for blocks S and H and the
pulley.
s
= Ma =
mM
M +
3
2
m
g
m
a
α =-a/r
r
b) ( 10 pts.) Find the linear acceleration of the rope.
)
c) ( 9 pts.) Find the magnitude of tension in the rope pulling on block S.
T
s
= Ma =
mM
M +
3
2
m
g
m
a
α =-a/r

Problem 4 (26 pts) As shown in the figure, an overhead view of a thin uniform rod of length
0.80 m and mass M = 1.0 kg rotating horizontally at angular speed 20 rad/s about an axis
through its center. A particle of mass M /3 initially attached to one end is ejected from the rod by
a small explosion and travels along a straight path that is perpendicular to the rod at the instant of
ejection. The particle's final speed v
p
(after the ejection) is 11.0 m/s.
a) ( 6 pts. ) What is the angular momentum (magnitude and
direction) of the particle about the center of rod at the
moment before the ejection?
)